Compute magnetic flux density: a flux of 5.5 µWb passes through a cross-sectional area of 6 × 10^–3 m^2. What is B?
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A917 µT
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B91.7 µT
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C9.7 T
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D91 T
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E0.917 T
Answer
Correct Answer: 917 µT
Explanation
Introduction / Context:Flux density B measures how concentrated magnetic flux Φ is over an area A. It is directly used in core design, sensor calibration, and magnetic circuit analysis. Converting units carefully (microwebers to webers) and applying the B = Φ / A definition are the keys here.
Given Data / Assumptions:
- Magnetic flux Φ = 5.5 µWb = 5.5 * 10^-6 Wb.
- Cross-sectional area A = 6 * 10^-3 m^2.
- Uniform distribution of flux over the area (standard assumption for calculation).
Concept / Approach:Use the fundamental relation B = Φ / A. Then convert the resulting tesla value into microtesla (1 T = 10^6 µT) to match typical engineering magnitudes for small flux/large area scenarios.
Step-by-Step Solution:
Write formula: B = Φ / A.Insert values: B = (5.5 * 10^-6 Wb) / (6 * 10^-3 m^2).Compute ratio: 5.5 / 6 = 0.9167; 10^-6 / 10^-3 = 10^-3.So B ≈ 0.9167 * 10^-3 T = 9.167 * 10^-4 T.Convert to microtesla: 9.167 * 10^-4 T = 916.7 µT ≈ 917 µT.Verification / Alternative check:Dimensional check: Φ in Wb divided by A in m^2 yields Wb/m^2, which equals tesla. Magnitude check: small flux over millimeter-scale area gives sub-millitesla values; hundreds of microtesla is reasonable.
Why Other Options Are Wrong:
- 91.7 µT: Off by a factor of 10 due to a power-of-ten slip.
- 9.7 T or 91 T: Unrealistically large; would imply extreme fields not supported by the given micro-weber flux and millimeter-scale area.
Common Pitfalls:
- Mistaking µWb for Wb, causing six orders of magnitude error.
- Forgetting to divide by the area in square meters.
Final Answer:917 µT